Ψs = -iCRT p + q = 1
AP BIOLOGY
QUANTITATIVE
SKILLS
+
pH = -log[H ]
C1V1 = C2V2
V = /3 r
dN/dt = r N
G = H - TS
pH = -log[H+]
K=°C + 273
Ψ = Ψp + Ψs
G = H - TS
4
3
max
dN/dt = rmaxN
p + 2pq + q = 1
2
2
CONTENTS
AP Biology Equations and Formulas ......................................................................................................................................3
Graphing .............................................................................................................................................................................................5
Data Analysis ....................................................................................................................................................................................7
Hypothesis Testing ........................................................................................................................................................................7
Mathematical Modeling................................................................................................................................................................8
Worksheet #1: Basic Statistical Tests ....................................................................................................................................9
Worksheet #2: Chi-Square and Punnett Square ............................................................................................................. 10
Worksheet #3: Hardy-Weinberg A....................................................................................................................................... 11
Worksheet #4: Hardy-Weinberg B ....................................................................................................................................... 12
Worksheet #5: Populations A................................................................................................................................................. 13
Worksheet #6: Populations B................................................................................................................................................. 14
Worksheet #7: Temperature Coefficient ........................................................................................................................... 15
Worksheet #8: Dilutions .......................................................................................................................................................... 16
Worksheet #9: SA:V.................................................................................................................................................................... 17
Worksheet #10: Water Potential .......................................................................................................................................... 18
Worksheet #11: Gibbs Free Energy Basics ....................................................................................................................... 19
Worksheet #12: Gibbs Free Energy Application ............................................................................................................ 21
Worksheet #13: Primary Productivity ............................................................................................................................... 22
Worksheet #14: pH and Metric System ............................................................................................................................. 23
Worksheet #15: Grid-In Practice .......................................................................................................................................... 24
Worksheet #16: Mixed Review .............................................................................................................................................. 26
2|Page
AP B IOLOGY E QUATIONS AND F ORMULAS
3|Page
4|Page
G RAPHING
One of the best ways to communicate the results of a scientific investigation is graphing, or creating an
effective visual representation (a graph) of the data that have been counted, measured, and calculated.
Investigators often can easily see patterns in a carefully crafted visual display that may not be as readily
apparent in a data table of numbers. Visual displays also can clarify how two measured variables affect
each other.
The AP Biology laboratory manual is designed to encourage students to ask their own questions by
designing and carrying out investigations. This process of inquiry requires data analysis and
communication of results. The data collected to answer questions generated by students will generally
fall into three categories: (1) normal or parametric data, (2) nonparametric data, and (3) frequency or
count data. Normal or parametric data are measurement data that fit a normal curve or distribution.
Generally, these data are in decimal form. Examples include plant height, body temperature, and
response rate. Nonparametric data do not fit a normal distribution, may include large outliers, or may
be count data that can be ordered. A scale such as big, medium, small (qualitative) may be assigned to
nonparametric data. Frequency or count data are generated by counting how many of an item fit into a
category. For example, the results of a genetic cross fit this type of data as do data that are collected as
percentages.
There are five types of graph you need to understand: bar graphs, box-and-whisker plots, pie charts,
scatter graphs and mosaic charts.
A. Bar graphs are graphs used to visually compare two samples of categorical or count data. Bar
graphs are also used to visually compare the calculated means with error bars of normal data
(Figure 1).
B. Scatter plots are graphs used to explore associations between two variables visually.
C. Box-and-whisker plots allow graphical comparison of two samples of nonparametric data (data
that do not fit a normal distribution).
D. Histograms, or frequency diagrams, are used to display the distribution of data, providing a
representation of the central tendencies and the spread of the data.
E. Mosaic charts are modified bar graphs that can show multiple axes simultaneously allowing a
more complete comparison.
Elements of effective graphing
A. Title: must inform the reader about the experiment and tell the reader exactly what is being
measured
B. Type: the reader must be able to easily discern the type of graph
C. Axes: must be clearly labeled with units
a. The x axis is the independent variable
b. The y axis is the dependent variable
c. Intervals must be uniform
d. It is not necessary to label every interval
e. Labels, including units, should allow the readier ti easily see the information
D. Multiple conditions: more than one condition can be present in a graph, however, they need to
be clearly labeled and a key must be present. This is the preferable method for comparing
multiple experiments that differ by only a single variable.
E. Origin: the origin of the graph must be clearly labeled whether it is at (0,0) or not.
5|Page
F. Standard error: you may include standard error bars to inform the reader of the accuracy of
your data collection.
Parametric Test
(Normal Data)
Non Parametric
Tests
Frequency
Tests (Counts)
Mean,
Standard
Deviation,
Error 95% Ci
Median,
Quartiles,
Interquartile
Range
Percent by
Category
Bar Graph
Box-andWhisker Plot
Bar Graph or
Pie Chart
2 Groups
Unpaired TTest
Mann Whitney
U-Test
≥ 2 Groups
Anova
Kruskal-Wallis
Test
Descriptive Statistics
Graph Type
Comparative
Statistics
Independent
Samples
2 Groups
Paried T-Test
Wilcoxon Test
≥ 2 Groups
Matched Anova
Friedman Test
Graph Type
Scatter Plot
Scatter Plot
Mosaic Chart
Test For Association
Pearson
Correlation
Spearman Rank
Correlation
Chi-Square Test
For Association
Linear Relationship
Linear
Regression
-
-
Matched
Samples
Association
Statistics
Source: Redrawn from “Statistics for AS Biology,” available as part of a download at:
http://www.heckmondwikegrammar.net/index.php?highlight=introduction&p=10310
6|Page
Chi-Square Test
D ATA A NALYSIS
1. Most numeric data falls into one of two categories: measurements or counts
2. Measurements: used to compare a quantitative data point to a universal standard
a. Continuous data: infinite number of potential measurements over a given range
b. Discrete data: limited number of possible measurements over a given range
3. Count data: recordings of categorical data
4. Descriptive statistics: enables reader to estimate important parameters of the data set and
determine a confidence interval
a. Examples: standard deviation, mean, median, mode
5. Inferential statistics: uses tools that rely on probability theory and an understanding of
distributions to determine precise estimations
H YPOTHESIS T ESTING
1. Statistical hypothesis testing focuses on trying to reject a null hypothesis.
a. A null hypothesis is a statement explaining that the underlying factor or variable is
independent of the observed phenomenon.
b. Alternative to the null hypothesis is a statement that the underlying factor or variable is not
independent of the observed phenomenon.
Possible Outcomes of Hypothesis Testing
Investigator action
Null hypothesis is true
Null hypothesis is false
Rejects the null hypothesis
Type I error (false positive)
Correct
Fails to reject null hypothesis
Correct
Type II error (false negative)
1. We use a critical (p) value (usually 95% sure of answer).
a. Using this system, there is only a 5% chance of making a type I error.
2. Chi-square testing
∑
i
null hypothesis: there is no difference between (the item being studied) and (random
chance)
b. degrees of freedom = number of samples - 1
c. use the 0.05 value for your critical value
(a) if the value is higher than the critical value- reject null hypothesis
(b) if the value is lower than the critical value-fail to reject null hypothesis
7|Page
M ATHEMATICAL M ODELING
Process of creating mathematical or computer based representations of the structure and interactions
of complex systems
1. Models are formed after experimentation and ask these types of questions
a. What can we measure
b. What should we measure
c. What are the relevant variables
d. What are the simplest informative models we can build
2. Aspects of models
a. Introducing power of the model
(a) Approximating real world conditions
b. Introducing limitations of the model
(a) Assumptions
(b) Simplifications
3. Components of mathematical models
a. Examine a system to identify which variables seem to be most likely to have an effect
b. Develop graphical or physical models to capture the essence of the phenomenon.
c. Translate the model into a “word equation.”
d. Translate word equations into formal equations
e. Implement the model on a computer
f. Evaluate, revise, extend the model
(a) Look at the basic assumptions, can they be eliminated?
(b) Look at the simplification, can it be minimized?
(c) Look at the approximation, can it be improved?
8|Page
W ORKSHEET #1: B ASIC S TATISTICAL T ESTS
Mode = value that occurs most frequently
Median = middle value
Mean = average
Range = dispersion of data points (value obtained by subtracting
the smallest observation from the greatest observation)
( xi  x ) 2
SD=
n 1
s
SE x 
n
standard deviation
standard mean error
̅ = sample mean
n = size of sample
s= sample standard deviation
o= observed results
e=expected results
1 n
x   xi
n i 1
mean
Example problem:
One of the lab groups collected the following data for the heights (in cm) of their Wisconsin Fast
Plants:
5.4
7.2
4.9
9.3
7.2
8.1
8.5
5.4
7.8
10.2
Find the mode, median, mean, and range. Show your work where necessary.
Mode(s):___________ ___
Median: ___________ ___
Mean: ___________ ___
Range: ___________ ___
Find the standard deviation by filling in the following table.
Heights (x)
5.4
7.2
4.9
9.3
7.2
8.1
8.5
5.4
7.8
10.2
Mean
(x )
xx
(x  x)2

( x  x ) 2
Standard deviation:
Interpret the standard deviation in the context of the problem.
What is the standard mean error? Calculate it for this data set.
9|Page
W ORKSHEET #2: C HI -S QUARE AND P UNNETT S QUARE
Formulas:
 ( o  e) 2
 e
2
Chi Square    



o = observed individuals with observed genotype
e = expected individuals with observed genotype
Degrees of freedom equals the number of distinct possible outcomes minus one
Degrees of
Freedom
p
1
2
3
4
5
6
7
8
0.05
3.84
5.99
7.82
9.49
11.07
12.59
14.07
15.51
0.01
6.64
9.32
11.34
13.28
15.09
16.81
18.48
20.09
Example problem:
Wisconsin Fast Plants have two very distinctive visible traits (stems and leaves). Each plant will either
have a purple (P) or green (p) stem and also have either have green (G) or yellow (g) leaves. Suppose that
we cross a dihybrid heterozygous plant with another plant that is homozygous purple stem and
heterozygous for the leaf trait. Make a Punnett square to figure out the expected ratios for the phenotypes
of the offspring.
Suppose a class observed that there were 234 plants that were purple stem/green leaves and 42 that were
purple stem/yellow leaves. Does this provide good evidence against the predicted phenotype ratio?
Using your understanding of genetics, what might be one reason why the class got these results?
10 | P a g e
W ORKSHEET #3: H ARDY -W EINBERG A
Formulas:
p2 + 2pq + q2 = 1
p+q=1
p = frequency of the dominant allele in a population
q = frequency of the recessive allele in a population
For people, being right handed (R) is the dominant trait over being left handed (r). Suppose there is a
sample of 20 people that reveals the following genotypes:
(RR)
(Rr)
(Rr)
(rr)
(RR)
(Rr)
(Rr)
(Rr)
(rr)
(RR)
(Rr)
(RR)
(RR)
(Rr)
(RR)
(RR)
(Rr)
(rr)
(RR)
(Rr)
What percentage of the people are right handed? Left handed?
Find p and q and interpret each in the context of the problem.
Now suppose that we took another sample of 10 people. This time we only know their phenotypes.
(Right) (Left) (Right) (Right) (Right) ( Right) (Right) (Right) (Left) (Right)
What percentage of the people are right handed? Left handed?
Can you find p and q exactly? Why?
Estimate p and q and interpret each in the context of the problem.
Estimate how many of the right handed people are homozygous and how many are heterozygous.
11 | P a g e
W ORKSHEET #4: H ARDY -W EINBERG B
Formulas:
p2 + 2pq + q2 = 1
p+q=1
p = frequency of the dominant allele in a population
q = frequency of the recessive allele in a population
Example problem:
In 1988 the Garces Memorial High School student body was made up of 90% right handed students. Being
right handed (R) is the dominant trait over being left handed (r).
What is p and q for the population of 1990 GMHS High School students. Interpret each.
Find the percent of the student body in 1990 that are homozygous right handed, heterozygous right
handed, and left handed.
Fast forward to today at Garces. We took a random sample of 100 students today and found that 18 of
them were left handed.
What are the new p and q values? How do they compare with the values from 1990?
There are many reasons why this apparent change could have occurred. Come up the five you will be
expected to know and give an example for each: (Hint: Why did I choose 1988, the year I graduated?)
12 | P a g e
W ORKSHEET #5: P OPULATIONS A
Rate
Population Growth
Exponential Growth
Logistic Growth
dY/dt
dN/dt = B – D
dN
 rmax N
dt
dN
K N
 rmax N 

dt
 K 
dY = amount of change
K = carrying capacity
Notes
B = birth rate
D = death rate
N = population size
rmax = maximum per capita growth rate of population
dN
N change in population size
=
=
= population growth rate
t
dt
change in time
Example 1:
There are 300 falcons living in a certain forest at the beginning of 2013. Suppose that every year there are
50 falcons born and 30 falcons that die.
What is the population growth rate (include units)? Interpret the value.
What is the per capita growth rate of the falcons over a year? Interpret the value.
dN
 rmax N
dt
c. Fill in the table and construct a graph.
Year
Population
Year
2013
2019
2014
2020
2015
2021
2016
2022
2017
2023
2018
2024
Population
Find the average rate of change for the falcon
population from 2013 to 2018 (include units).
Interpret the value.
13 | P a g e
W ORKSHEET #6: P OPULATIONS B
Bakersfield had a population of 347,500 in the year 2010. The infrastructure of the city allows for a
carrying capacity of 450,000 people. rmax = .9 for Bakersfield.
a. Is the current population above or below the carrying capacity? Will the population increase or decrease
in the next year?
b. What will be the population growth rate for 2010 (include units)?
c. What will be the population size at the start of 2014.
d. Fill in the following table:
Year
Population size
at start of year
Population growth rate
(new people added)
2010
2011
2012
2013
2014
e. What happened to the population size over the years?
f. What happened to the population growth rate over the years?
g. f. Explain your answer from part (e) using what you know about carrying capacity.
h. g. Explain your answer from part (e) using the formula:
14 | P a g e
dN
K N
 rmax N 

dt
 K 
W ORKSHEET #7: T EMPERATURE C OEFFICIENT
k 
Q10   2 
 k1 
T2=higher temperature
T1 = lower temperature
k2= reaction rate at T2
k1=reaction rate at T1
Q10=factor by which the reaction rate increases when the temperature
increases by 10°C
10
T2 T1
R2 =R1 x Q10
The rate of metabolism of a certain animal at 10ºC, is 27 μL O2 g-1h-1.
1. What are its rates of metabolism at 20, 30, and 40 ºC if the Q10 is 2? If it is 2.5?
Temperature ºC
20
30
40
Temperature ºC
20
30
40
Rate2 if Q10 = 2
Rate2 if Q10 = 2.5
2. Graph the two tables above showing the effect of Temp on
reaction rate
Temperature
(ºC)
Rate of
Metabolism
(μLO2 g-1h-1.)
15
10
20
13.42
30
21.22
Q10
The table above reports the rates of metabolism of a species
at a series of ambient temperatures:
3. Calculate the Q10 values for each temperature interval
4. Within which temperature interval (15-20 or 20-30) is the rate of metabolism most sensitive to
temperature change?
5. For this species, would a Q10 calculated for 15 to 30 ºC be as useful as several for smaller temperature
ranges? Calculate that Q10 as part of your answer.
The reaction rate for a certain process at 14 ºC is 15 units/time. What would be the reaction rate at 20 ºC
if the Q10 = 1?
15 | P a g e
W ORKSHEET #8: D ILUTIONS
C1V1 = C2V2 aka. M1V1=M2V2
1M AgNO3= 1 mol AgNO3/L
C1 = original concentration of the solution, before it gets watered down or diluted.
C2 = final concentration of the solution, after dilution.
V1 = volume about to be diluted
V2 = final volume after dilution
For all dilution problems C1> C2, and V1< V2. It makes sense because to dilute, we add water.
Joe has a 2 g/L solution. He dilutes it and creates 3 L of a 1 g/L solution. How much of the
original solution did he use?
What is the molarity of a solution with 360 g glucose in 500 mL of distilled water?
Since Joe did such a good time before, the teacher asked Joe to make a set of solutions. For the
lab the students need 2-L of each NaCl stock solution at 1.0M, 0.75M, 0.50M, and 0.25M. If the
molar mass of NaCl is 58.45 g/mol, what are the directions for each of the solutions. Be specific
and show your calculations.
16 | P a g e
W ORKSHEET #9: SA:V
Surface area to Volume and Water Potential Review
Cells throughout the world have variable shapes and sizes. Because of this, and because
structure is designed around function, certain shapes are optimal for certain processes.
Analyze the following cells (units not to scale), and
determine the following…
Cell 1 (spherical) where the diameter is 6 mm
Vsphere = 4/3 π r3
Vrectangle = l w h
Asphere = 4 π r2
Arectangle = Σ (SA for each side)
Cell 2 (flat and rectangular) where the height is 0.5mm, length is 4mm, width is 2mm
Cell 3 (cube) where side length is 6 mm
Cell
Surface area
Volume
Surface area to
Volume Ratio
Cell 1
Cell 2
Cell 3
A) What is the surface area to volume ratio of each cell? Complete the table above.
B) Conclusion: Compare the ratios and explain why one cell would be more efficient than
another.
C) If the volume of two cells are identical, but one is a sphere and the other a cube, what are
their respective surface areas? Use an arithmetical example.
D) Are you made of lots of large cells or lots of small cells? Why? How do you grow in height?
E) Provide 5 specific examples of ways organisms use SA:V ratio to survive.
17 | P a g e
W ORKSHEET #10: W ATER P OTENTIAL
Ψ= ΨP + ΨS
ΨP= pressure potential; ΨS = solute potential
ΨS = -iCRT
i = ionization constant; C = molar concentration; R = 0.0831; T=Temp (K)
The water potential will be equal to the solute potential of a solution in an open container
i is 1.0 for sucrose because sucrose does not ionize in water
Water potential in potato cells was determined in the following manner. The initial masses of six
groups of potato cores were measured. The potato cores were placed in sucrose solutions of
various molarities. The masses of the cores were measured again after 24 hours. Percent changes
in mass were calculated. The results are shown below
Molarity of
Sucrose in
Beaker
0.0 M
0.2
0.4
0.6
0.8
1.0
Percent Change
in Mass
18.0
5.0
-8.0
-16.0
-23.5
-24.0
Graph these data. From
your graph, label where
the cells were hypotonic
and hypertonic.
Determine the apparent
molar concentration
(osmolarity) of the potato
core cells.
Looking at the water potential
equation,
Pressure potential is always (positive/negative), while solute
potential is always (positive/negative).
When Solution potential goes down (gets more negative), water
potential (increases/decreases)
When Pressure potential goes down (gets smaller), water potential
(increases/decreases)
When would the pressure in a cell rise? (Under what conditions?)
What would happen to the solute potential when
Concentration is increased (justify with
equation)? WHY?
What would happen to the solute potential when
Temperature is increased (justify with
equation)? WHY?
18 | P a g e
What would happen to the solute potential when
the dissolved substance is glucose vs. salt
(justify with equation)? WHY?
Why is water potential important for plants?
What are they lacking?
Predict what would happen to animal cells
placed in 0.0M and 1.0M concentration solution
W ORKSHEET #11: G IBBS F REE E NERGY B ASICS
ΔG = ΔH - T ΔS
What is Entropy (ΔS) = a measurement of ________________________________________________
When ΔS is positive this means there is ________________________________________________
When ΔS is negative this means there is ________________________________________________
What is ΔH? = a measurement of ________________________________________________
When ΔH is positive this means the reaction is ________________________________________________
When ΔH is negative this means the reaction is ________________________________________________
What is Gibbs Free energy? = a measurement of ________________________________________________
When ΔG is positive this means the reaction will happen ____________________________________________
When ΔG is negative this means the reaction will happen ___________________________________________
ΔG (Joules)
ΔH (Joules)
T (Kelvin)
ΔS (J/K)
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
300
300
300
300
300
300
300
300
300
300
5
5
5
5
5
5
5
5
5
5
What happens to ΔG when ΔH goes up ? WHY?
What happens to ΔG when ΔH goes down ? WHY?
19 | P a g e
ΔG
ΔH
T
ΔS
1700
1700
1700
1700
1700
1700
1700
1700
1700
1700
300
310
320
330
340
350
360
370
380
390
5
5
5
5
5
5
5
5
5
5
ΔH
T
ΔS
7500
7500
7500
7500
7500
7500
7500
7500
7500
7500
300
300
300
300
300
300
300
300
300
300
5
10
15
20
25
30
35
40
45
50
What happens to ΔG when T goes up ? WHY?
What happens to ΔG when T goes down ? WHY?
ΔG
What happens to ΔG when ΔS goes up ? WHY?
What happens to ΔG when ΔS goes down ? WHY?
Complete the sentences below.
As the reaction requires less and less energy, its spontaneity will (increase, decrease).
As randomness increases, the free energy will (increase, decrease) because ______________
__________________________________________________________________________
20 | P a g e
W ORKSHEET #12: G IBBS F REE E NERGY A PPLICATION
Energies are usually given as standard free energies of hydrolysis. For example
glucose-6-phosphate + water → glucose + Pi
has ΔG° = -4.0 kcal/mole (-16.5 kJ/mole) under standard conditions. Therefore, the opposite
reaction, the phosphorylation of glucose, is unfavored. However, the phosphorylation of
glucose occurs readily in the cell, catalyzed by the enzyme hexokinase:
glucose + ATP → glucose-6-phosphate + ADP + Pi
The other half of the phosphorylation reaction is the hydrolysis of ATP to yield ADP and
inorganic phosphate (Pi): ATP + H2O → ADP + Pi
under standard conditions has ΔG° = -7.3 kcal/mole (-31 kJ/mole).
The standard free energy change of the reaction can be determined by adding the two free
energies of reaction:
Glucose + Pi → glucose-6-phosphate + H2O
and ΔG° =+-4.0 kcal/mole
Note that the reaction as written is unfavored; its free energy change is positive. Another way
of stating this is that the reaction is endergonic, that is, the reaction involves a gain of free
energy.
For the exergonic hydrolysis of ATP (the reaction involves a loss of free energy):
ATP + H2O → ADP + Pi
ΔG° = -7.3 kcal/mole
The two reactions are summed:
Glucose + ATP → glucose-6-phosphate + ADP + Pi
ΔG° = -3.3 kcal/mole
This is a simple example of energetic coupling, where an unfavorable reaction is driven by a
favorable one.
Coupling doesn't occur all by itself. In this example, if this experiment were set up so that the
ATP would have to be hydrolyzed in one tube and the
glucose phosphorylated in another, no coupling would be
possible. Coupling can occur only when the partial
reactions are part of a larger system. In this example,
coupling occurs because both partial reactions are carried
out by the enzyme hexokinase. In other cases, coupling can
involve membrane transport, transfer of electrons by a
common intermediate, or other processes. Another way of
stating this principle is that coupled reactions must have some component in common.
1.
2.
3.
The “orderliness” of your body is not favored by free energy. Explain (in terms of free energy
and disorder) why you need to perform digestion?
Why does decomposition of a dead animal happen in terms of energy? What would happen if
we increase temperature? Why do we freeze food?
Explain why plant cells need light to build sugar (in terms of energy).
21 | P a g e
W ORKSHEET #13: P RIMARY P RODUCTIVITY
mg O2 0.698mL mL O2
x

L
mg
L
mL O2 0.536 mg C fixed mg C fixed
x

L
mL O2
L
One can determine Primary Productivity by measuring dissolved oxygen in the water (as it is
hard to measure it in the air)
1 ml of O2 = 0.536 mg of Carbon assimilated
mg O2/L x 0.698 = ml O2/L; ml O2/L x 0.536 = mg carbon fixed/L
6CO2 + 6H2O → C6H12O6 + 6O2
Fill in the table and Graph Net and Gross Productivity vs. % of light
% light
DO2
(mg O2/L)
Initial
Dark
100%
65%
25%
10%
2%
8.4
6.2
10.2
9.7
9.0
8.5
7.1
Gross PP =
DO2-dark
(mg O2/L)
—
—
Net PP =
DO2 -initial
(mg O2/L)
—
—
Gross carbon fixed in mg C/L
Gross PP x 0.698 x 0.536
—
—
Using your data table, what seems to be the trend as the % of light decreases? WHY?
Using your data table, what seems to be the trend as
the % of light increases? WHY?
Where would you say this organism is using as much
energy as they are making? WHY?
Using your table and graph, explain why most of the
time there are bigger plants on land than in the sea?
Explain this in terms of evolution.
22 | P a g e
W ORKSHEET #14: P H AND M ETRIC S YSTEM
pH = -log[H+]
pOH = -log[OH-]
pH + pOH = 14 recall [H+] is really [H3O+]
Which is more acidic? [H+] 1.0 x 10-8 or 1.0 x 10-12
Which is more basic? [H+] 1.0 x 10-6 or 1.0 x 10-3
The pH of stomach acid is about 1.5. what is the [H+]?
Blood has a pH of about 7.40. What is the [H+]?
[H+]
1 000 000
1 000
100
10
1
0.1
0.01
0.001
0.000 001
0.000 000 001
0.005
0.05
0.000 026
Scientific notation
pH
Metric prefix
—
—
—
—
—
Write answers in scientific notation: (NO CALCULATORS)
4.00x105 x 2.00x103
8.00x107 / 2.00x103
4.00x10-5 x 2.00x10-3
8.00x107 / 2.00x10-3
4.00x105 x 2.00x10-3
8.00x10-7 / 2.00x103
4.00x10-5 x 2.00x103
8.00x10-7 / 2.00x10-3
When you divide in scientific notation, you need to _______________________ the exponents.
When you multiply in scientific notation you need to _______________________ the exponents.
23 | P a g e
W ORKSHEET #15: G RID -I N P RACTICE
You will have questions that use a grid-in. in general, these questions should
be fairly straight forward. Here are a few examples.
-
.
/
/
/
.
.
.










.










There are 252 deer in a population. There is no net immigration or
emigration. If 47 deer die and 32 deer are born in one month, what is the
population size at the end of the month? Round to the nearest whole
number.
Solution: 252-47+32=237 All answers below are correct
2 3 7
-
.
/
/
/
.
.
.










2 3 7
.
-










.
/
/
/
.
.
.




















.










Correct ways to write one-half
0 . 5
include:
-
.
/
/
/
.
.
.










24 | P a g e










.










. 5
-
.
1 / 2
/
/
/
.
.
.










.










-
.
/
/
/
.
.
.










.










SAMPLE QUESTIONS SUITABLE FOR GRID-IN RESPONSES.
1. In snapdragons (Antirrhinum), the phenotype for flower color is governed by two alleles – red
(R) and white (W). Heterozygous individuals have pink flowers. Two pink individuals are
crossed to produce 465 offspring. Calculate how many of these offspring are expected to have
the red phenotype. Round your response to the nearest whole number.
2. The molar concentration of a sugar solution in an open beaker has been determined to be 0.3M.
Calculate the solute potential at 27 degrees Celsius. Round your answer to the nearest tenths.
3. The net annual primary productivity of a particular wetland ecosystem is found to be 8000
kcal/m2. If respiration by the aquatic producers is 12,000 kcal/m2 per year, what is the gross
annual primary productivity for this ecosystem in kcal/m2 per year? Round to the nearest
whole number.
Respiration
Temp
rate
4. Data taken to determine the effect of temperature on the rate of
(°C)
(per
min)
respiration in a goldfish is given in the table to the right. Calculate Q10 for
16
16
this data. Round to the nearest whole number.
21
22
5. Joe has a 2 g/L solution. He dilutes it and creates 3 L of a 1 g/L solution. How much of the
original solution did he dilute (in L)? Round to the nearest tenths.
6. What is the hydrogen ion concentration of a solution of pH 8? Round to the nearest whole
number.
7. What is the SA/V for this cell if r = 3m? Round your answer to the nearest
hundredth.
8. A census of birds nesting on a Galapagos Island revealed that 24 of them show a rare recessive
condition that affected beak formation. The other 63 birds in this population show no beak
defect. If this population is in HW equilibrium, what is the frequency of the dominant allele?
Give your answer to the nearest hundredth
O2
Time
9. There are 2000 mice living in a field. If 1000 mice are born each month
produced
(min)
and 200 mice die each month, what is the per capita growth rate of mice
(mL)
over a month? Round to the nearest tenths.
1
2.3
2
3.6
10. Hydrogen peroxide is broken down to water and oxygen by the enzyme
3
4.2
catalase. The data were taken over 5 minutes. What is the rate of
4
5.5
enzymatic reaction in mL/min from 2 to 4 minutes? Round to the nearest
5
5.9
hundreds
11. The following data were collected on the behavior of
preschoolers. Some were spanked, some were given time-outs
and some were given no discipline. Five years later teachers
were asked to keep track of the behavior issues of these
children. Find the chi-square.
no discipline
time-outs
spanking
#
misbehaviors
40
34
26
25 | P a g e
W ORKSHEET #16: M IXED R EVIEW
1. Students used D. melanogaster for a genetics lab. They chose to look at two traits to see if they
were linked. They chose eye color and wing shape. Red is the dominant eye color and normal is
the dominant wing shape. After beginning with a P generation of EEWW and eeww, they used
the F2 generation. They got the following results.
Red eyes, normal wings: 184
Red eyes, stunted wings: 12
Yellow eyes, normal wings: 45
Yellow eyes, stunted wings: 68
Are these genes linked? Support your answer.
2. Albinism is a rare genetically inherited trait that is only expressed in the phenotype of
homozygous recessive individuals (aa). The most characteristic symptom is a marked
deficiency in the skin and hair pigment melanin. This condition can occur among any human
group as well as among other animal species. The average human frequency of albinism in
North America is only about 1 in 20,000. What percentage of people carry this gene?
3. If a cell’s ΨP = 3 bars and its ΨS = -4.5 bars, what is the resulting Ψ?
a) The cell is placed in a beaker of sugar water with ΨS = -4.0 bars. In which direction will the
net flow of water be?
b) The original cell 1 is placed in a beaker of sugar water with ΨS = -0.15 MPa (megapascals).
We know that 1 MPa = 10 bars. In which direction will the net flow of water be?
4. A change in pH from 3 to 5 means what in terms of [H+]?
5. What is the surface area of a cube that has the same volume as a sphere with a surface area of
100 cm2?
6. The lab kit you got only has 500 mL of 6.0 M HCl, but you need 500 mL of 0.2M HCl. How could
you make what you need without wasting any of the stock solution?
7. The following data were collected on the behavior of preschoolers.
Some were spanked, some were given time-outs and some were given
no discipline. Five years later teachers were asked to keep track of the
behavior issues of these children. Did the punishment reflect improved
behavior in upper elementary grades? (You did the math earlier (page ,
now draw the conclusion!)
26 | P a g e
no discipline
time-outs
spanking
#
misbehaviors
40
34
26
8. Calculate the mean, median, mode and standard deviation for this data set.
12
14
18
12
14
19
21
8
17
6
9. Graph the following scenario. CORRECTLY!
Explain what the graph tells you about each plant.
5
9
1
7
Depth (m)
2
5
10
16
25
30
2
6
Bubbles per
minute
(Plant A)
29
32
45
32
20
10
12
18
16
8
Bubbles per
minute
(Plant B)
21
27
40
50
34
20
27 | P a g e
10. In a population of 600 squirrels, the per capita birth rate in a particular period is 0.06 and the
per capita death rate is 0.12.
a. What is the per capita growth rate of the population? Round to the nearest hundredth.
b. What is the actual number of squirrels that die during this particular period?
c. What is the actual number of squirrels that are born during this period?
11. The doubling time of a population of plants is 12 years. Assuming that the initial population is
300 and that the rate of increase remains constant, how large will the population be in 36
years?
12. There are 780 turkeys living in Merriam Township, which is 92 acres in size. The birth rate is
0.472 turkeys/year per capita. The death rate is 0.331 turkeys/year per capita.
a. What is the population density? Round to the nearest tenth.
b. What is dN/dt? Round to the nearest whole number.
c. Predict N after one year, assuming dN/dt stays constant. Round to the nearest whole
number.
13. One dandelion plant can produce many seeds leading to a high growth rate for dandelion
populations. If a population of dandelions is currently 40 individuals and rmax = 0.2
dandelions/month per capita, predict how many dandelions would be in this population after 4
months. Round to the nearest whole number.
14. A hypothetical population has a carrying capacity of 1,500 individuals and rmax is 1.0. Fill out the
following table. Round all answers to the nearest whole number. Explain the results.
Population
Show Work Here
1250
1500
1750
2000
15. Determine the Q10 value for the heart rate in Daphnia, the water flea.
28 | P a g e
Temperature (Co)
Average Heart Rate
(beats per minute)
14
127
20
162
26
197
Population Growth
16. What is the primary productivity of this ecosystem at each of the specified light levels?
% light
DO2
(mg O2/L)
Initial
0%
100%
85%
55%
20%
12%
7.4
5.2
9.2
8.7
8.0
7.5
6.1
Gross PP =
DO2-dark
(mg O2/L)
—
—
Net PP =
DO2 -initial
(mg O2/L)
—
—
Gross carbon fixed in mg C/L
Gross PP x 0.698 x 0.536
—
—
17. Calculate the population sizes between the following groups. Each begins with 1,500 individuals
and has a maximum growth rate per capita of 0.4. The first population (population A) does not
have a carrying capacity while the second (population B) has a carrying capacity of 50,000. Any
population that reaches twice the carrying capacity goes locally extinct. Create a model on Excel
that will show the populations for the next 100 years. Challenge: make the model able to
accommodate changes to the rmax, initial populations, and carrying capacity. Alternately, you can
do the work by hand for 30 years. (Hint: use the equations!)
29 | P a g e